Bottom Line:
Although most studies in optics have focussed on how nonlinearity can drive rogue wave emergence, purely linear effects have also been shown to induce extreme wave amplitudes.Intensity peaks satisfying statistical criteria for rogue waves are seen especially in the case of the caustic network, and are associated with broader spatial spectra.In addition, the electric field statistics of the intermediate pattern shows properties of an "optical sea" with near-Gaussian statistics in elevation amplitude, and trough-to-crest statistics that are near-Rayleigh distributed but with an extended tail where a number of rogue wave events are observed.

ABSTRACTThere are many examples in physics of systems showing rogue wave behaviour, the generation of high amplitude events at low probability. Although initially studied in oceanography, rogue waves have now been seen in many other domains, with particular recent interest in optics. Although most studies in optics have focussed on how nonlinearity can drive rogue wave emergence, purely linear effects have also been shown to induce extreme wave amplitudes. In this paper, we report a detailed experimental study of linear rogue waves in an optical system, using a spatial light modulator to impose random phase structure on a coherent optical field. After free space propagation, different random intensity patterns are generated, including partially-developed speckle, a broadband caustic network, and an intermediate pattern with characteristics of both speckle and caustic structures. Intensity peaks satisfying statistical criteria for rogue waves are seen especially in the case of the caustic network, and are associated with broader spatial spectra. In addition, the electric field statistics of the intermediate pattern shows properties of an "optical sea" with near-Gaussian statistics in elevation amplitude, and trough-to-crest statistics that are near-Rayleigh distributed but with an extended tail where a number of rogue wave events are observed.

f2: Numerical simulations showing (a) partially-developed speckle and (b) a caustic network. For each case, (i) shows the computed intensity distribution; (ii) shows a zoom over a more limited region looking down on the pattern; (iii) shows a slice of the applied phase distribution to the SLM at y = 0; (iv) shows the calculated spatial spectrum. Intensities in (b) are normalised relative to the maximum intensity for the partially-developed speckle in Fig. 2a. Note the different intensity scales used between (a,b).

Mentions:
Results showing numerical simulations modelling propagation through the experimental setup are shown in Fig. 2. The simulations discretized the incident field profile to match the experimental SLM pixellation, upon which a smoothed random phase function was applied (see Methods). The Angular Spectrum of Plane Waves method34 was then used to numerically propagate this beam through the optical system described above. No paraxial approximations were made in the modelling.

f2: Numerical simulations showing (a) partially-developed speckle and (b) a caustic network. For each case, (i) shows the computed intensity distribution; (ii) shows a zoom over a more limited region looking down on the pattern; (iii) shows a slice of the applied phase distribution to the SLM at y = 0; (iv) shows the calculated spatial spectrum. Intensities in (b) are normalised relative to the maximum intensity for the partially-developed speckle in Fig. 2a. Note the different intensity scales used between (a,b).

Mentions:
Results showing numerical simulations modelling propagation through the experimental setup are shown in Fig. 2. The simulations discretized the incident field profile to match the experimental SLM pixellation, upon which a smoothed random phase function was applied (see Methods). The Angular Spectrum of Plane Waves method34 was then used to numerically propagate this beam through the optical system described above. No paraxial approximations were made in the modelling.

Bottom Line:
Although most studies in optics have focussed on how nonlinearity can drive rogue wave emergence, purely linear effects have also been shown to induce extreme wave amplitudes.Intensity peaks satisfying statistical criteria for rogue waves are seen especially in the case of the caustic network, and are associated with broader spatial spectra.In addition, the electric field statistics of the intermediate pattern shows properties of an "optical sea" with near-Gaussian statistics in elevation amplitude, and trough-to-crest statistics that are near-Rayleigh distributed but with an extended tail where a number of rogue wave events are observed.

ABSTRACTThere are many examples in physics of systems showing rogue wave behaviour, the generation of high amplitude events at low probability. Although initially studied in oceanography, rogue waves have now been seen in many other domains, with particular recent interest in optics. Although most studies in optics have focussed on how nonlinearity can drive rogue wave emergence, purely linear effects have also been shown to induce extreme wave amplitudes. In this paper, we report a detailed experimental study of linear rogue waves in an optical system, using a spatial light modulator to impose random phase structure on a coherent optical field. After free space propagation, different random intensity patterns are generated, including partially-developed speckle, a broadband caustic network, and an intermediate pattern with characteristics of both speckle and caustic structures. Intensity peaks satisfying statistical criteria for rogue waves are seen especially in the case of the caustic network, and are associated with broader spatial spectra. In addition, the electric field statistics of the intermediate pattern shows properties of an "optical sea" with near-Gaussian statistics in elevation amplitude, and trough-to-crest statistics that are near-Rayleigh distributed but with an extended tail where a number of rogue wave events are observed.